Do you think Romeo is serious when he says that his life were better ended by their hate than death prolonged wanting of Juliet's love? Why or why not?

Romeo has been using hyperbole, or overstatement, in order to—I think—impress Juliet with the strength of his feelings for her. When she expresses her concern that her family would kill him if they found him in her garden, he assures her that there is "more peril in [her] eye / Than twenty of their swords" (2.2.76–77). By saying this, Romeo implies that Juliet could do much more harm to him than their swords can do; this is an exaggeration between Juliet could make Romeo feel really, really sad if she refuses his declarations of love, but her family can actually kill him. He tells her, "Look thou but sweet, / And I am proof against their enmity" (2.2.77–78). In other words, he says that if she looks upon with him favor, he can withstand all of their hate and violence. Again, this is an exaggeration. He says,

My life were better ended by their hateThan death prorogued, wanting of thy love. (2.2.82-83)

He means that it would be better for him to die quickly, the result of her family's hate, than for him to pine for death because Juliet does not love him. He doesn't want to live without her love. Again, he's probably exaggerating because he wouldn't actually choose death over life without the love of a girl he only just met, but he wants her to feel that he is sincere and passionate, and this is a good way to convince her.